The interface coupling of the gas dynamics equations C. Chalons, P.-A. Raviart, N. Seguin Abstract We investigate the one-dimensional coupling of two systems of gas dy- namics at a fixed interface. The coupling constraints consist in requiring the continuity of a system of nonconservative variables at the interface. Since we are dealing with hyperbolic systems, weak coupling conditions are proposed. The existence and the uniqueness of the solutions of the coupled Riemann problem are investigated. Several examples of solutions satisfying the weak coupling conditions are contructed, either continu- ous or discontinuous with respect to the nonconservative variables at the interface. Introduction. The problem of coupling various mathematical models described by systems of partial differential equations is a topic of increasing importance. It arises for instance in the modelling of complex industrial devices in Engineering. The device is divided into different parts which are modelled using different approx- imations. It then remains to couple these models at the interfaces separating the various parts of the device for obtaining a global mathematical model. As a constraint, the coupling procedures have to be as local as possible in order to be easily implemented numerically. Such coupling problems are encountered in several applications. First, they naturally arise in Thermohydraulics in connection with the modelling of the primary coolant circuit of a pressurized water reactor in a nuclear power plant. Various multiphase fluid models are used involving systems of partial differential equations having a variable number of equations supplemented with various closure relations. Similar situations appear also in the modelling of two-fluid (or multi-fluid) flows where the dynamics is provided by the one of the fluids. The two fluids possess their own equation of state and are coupled at a moving interface. See [AK01] and the large literature on this subject. We can also mention the coupling problems arising in networks [CG06, BHK06a, BHK06b] and traffic flows [GP06a, GP06b, HR06] which have deserved a growing interest in the last few years. In this paper, we are indeed concerned with the applications to nuclear re- actors 1 . The overall coupling problem in this context is a very difficult and 1 The authors of the present paper are involved in a joint research program on multiphase flows between CEA and University Pierre et Marie Curie-Paris6 (see [ACC + 05a, ACC + 05b, ACC + 06b, ACC + 06a, ACC + 06c] and the references therein) in the framework of the Neptune project. 1